Nonlinear Mechanics of Suspended Ultra-thin Membranes: From Molecular Dynamics to Continuum Mechanics

Ultra-thin drums play a crucial role in sensing applications due to their slender construction and relatively low bending rigidity. These properties render them highly sensitive to external forces. The emergence of graphene and other 2D materials has profoundly impacted the development of these devices, allowing for the creation of exceptionally thin membranes, even as thin as a single atomic layer. However, the extreme thinness of these structures introduces challenges, such as susceptibility to large deformations and nonlinear behaviour, making linear models unsuitable for mechanical analysis.

To fully harness the potential of ultra-thin resonators in practical applications, it is thus essential to comprehend their nonlinear mechanical behaviour thoroughly. Consequently, mathematical modelling and numerical simulations play a pivotal role in studying the nonlinear mechanics governing the motion and resonant behavior of these devices. This doctoral thesis investigates the nonlinear mechanics of ultra-thin membranes. Its primary objective is to develop analytical and numerical methodologies that will facilitate the future design and analysis of these structures for various applications...